Perfect 5ths' aren't Really Perfect

[DavC]

The human ears are imperfect in how they perceive pitch. They tend to hear flat in the higher register. To counter this, the octaves must be stretched beyond their normal pitches in order for the human ear to hear them correctly.

So actually , ... nothing is Perfect .. !??

 

[iiipopes]

I never understood why "dominant 7th" was called that... didn't seem superior in anyway to me to the major 7th... it always seemed like the maj 7th should be dominant if any... why do we need one to be dominant? What are we not saying about the other chords? That they are inferior and subordinate?

Who knows why this stuff is the way it is? Perfect 5ths and 4ths don't seem that great to me...

Just they way it was named and it stuck...

The dominant 7th chord is structured on the dominant note, named because it is the primary reinforcement note of the tonic chord of the scale. To use a C major scale as the example, the definition terms for the notes in the scale are:

C - tonic
D - supertonic (one note above the tonic)
E - mediant (or middle, between the tonic and the dominant)
F - subdominant (makes more sense when you go down the fifth to F, like changing to the IV chord in a blues song)
G - dominant (primary note enforcing the tonic)
A - submediant (middle between the tonic or octave and the subdominant)
B - leading tone
C - octave.

Since the G is the dominant of C, then the dominant 7th chord, GBDF, serves the primary function in Western common era music theory of pulling the melody back to the tonic CEGC chord. And so it goes.

 

[vickerekes]

Let me tell you... when you get a trombone ensemble together doing Renaissance & Baroque-style chorale pieces, if they're doing it in just intonation and everyone's good... it's really magical. You start getting overtones ringing that seem to come from the top of the concert hall.

Barbershop overtones ring like that.

 

[jdh3000]

The dominant 7th chord is structured on the dominant note, named because it is the primary reinforcement note of the tonic chord of the scale. To use a C major scale as the example, the definition terms for the notes in the scale are:

C - tonic
D - supertonic (one note above the tonic)
E - mediant (or middle, between the tonic and the dominant)
F - subdominant (makes more sense when you go down the fifth to F, like changing to the IV chord in a blues song)
G - dominant (primary note enforcing the tonic)
A - submediant (middle between the tonic or octave and the subdominant)
B - leading tone
C - octave.

Since the G is the dominant of C, then the dominant 7th chord, GBDF, serves the primary function in Western common era music theory of pulling the melody back to the tonic CEGC chord. And so it goes.

Seems like I've read that all before... long ago... Just terms like dominant 7th come up way more in the mainstream than supertonic, mediant, etc.

I knew it was so named for some reason, just in eveday language it sounds odd and just something that one accepts.

Good once in a while to see why things are called what they are called, like the etymology of words.

Thanks!

 

[pav]

"perfect" in musicological terms, and "perfect" in tuning terms, meaning two different things...

Our 12-semitone scale is a bodge - which we have got very used to! It is the musical equivalent of sweeping the room, and not getting rid of the dirt, but hiding it under the carpet ... a little bit here... a bit there... and there... and no-one will notice.. or WILL they?
Look at this youtube video - https://www.youtube.com/results?search_query=harry+partch+43+tone+scale

I am not just quoting theory... In the Edinburgh Festival a few years ago we went to a concert of Partch's music, on the instruments he designed... Our first thought was "that is slightly out of tune?" ; but by the end of the concert we realised it was MORE in tune than the music we normally hear!!!
So you need a bass with 43 frets to the octave...?

Or you could get involved with classical Turkish music, where the octave is divided into 53; I have heard a Turkish violinist, in London, play the western major scale, followed by the Turkish "Rast" scale, which is very very similar - but it sounded sweeter and better!

Until then, i guess we live with the bodge we are used to?

 

[Malcolm35]

I'm with the OP, This did not look like something I needed to get into, so I just call it 1, 3, 5, 7 or I-IV-V and moved on.

 

[byacey]

Barbershop overtones ring like that.

Likewise with string quartets.

 

[iiipopes]

Barbershop overtones ring like that.

Likewise with string quartets.

Indeed. And why tuning matters:

In the summer of 1984 I had a summer term at Emmanuel College, Cambridge, (the college's most famous graduate: John Harvard, yes, that's the one) taking legal history and international law. I asked the choir director of Great St. Mary's (you know - the famous chimes every quarter hour on just about every grandfather clock made - and adopted by Westminster, hence their name Westminster Quarters - Wikipedia) if I could sing in their choir while I was there. At first, taken aback by the brash American, said, "Right. Of course." And so I sang every Sunday and rehearsal that summer, including learning Anglican Chant for the psalms. The last Sunday I was there the choir was scheduled to caravan up to Ely Cathedral (famous for its octagon "lantern" at the crossing of the transepts) to sing evensong for the Bishop. On the anthem, I was the baritone, singing the dominant on the last chord. The bass sang the tonic; the tenor sang the octave. We locked. The chord caught the nave, which with its wooden ceiling isn't supposed to resonate that well. But it did, and the difference tone came back at us and resonated the entire cathedral, even though at only mezzo-forte volume. We looked at each other, wide-eyed. Even the bishop noticed. Yes, when a chord locks properly, it's like you are looking through the gate directly into heaven. Here is a picture in my cassock and surplice on that day, underneath the 10th century Saxon doorway that pre-dates and was incorporated into the choir of the cathedral (I was all of twenty-two and a half years old). The picture has unfortunately faded in the last thirty-six years.

 

[MVE]

"perfect" in musicological terms, and "perfect" in tuning terms, meaning two different things...

Our 12-semitone scale is a bodge - which we have got very used to! It is the musical equivalent of sweeping the room, and not getting rid of the dirt, but hiding it under the carpet ... a little bit here... a bit there... and there... and no-one will notice.. or WILL they?
Look at this youtube video - https://www.youtube.com/results?search_query=harry+partch+43+tone+scale

I am not just quoting theory... In the Edinburgh Festival a few years ago we went to a concert of Partch's music, on the instruments he designed... Our first thought was "that is slightly out of tune?" ; but by the end of the concert we realised it was MORE in tune than the music we normally hear!!!
So you need a bass with 43 frets to the octave...?

Or you could get involved with classical Turkish music, where the octave is divided into 53; I have heard a Turkish violinist, in London, play the western major scale, followed by the Turkish "Rast" scale, which is very very similar - but it sounded sweeter and better!

Until then, i guess we live with the bodge we are used to?

I’m going to disagree with this. The 12 tone system comes from the tonic/dominant relationship. Start with any tone(tonic), go up to the dominant that is “perfect” because it does not beat with the tonic, then use that tone as the tonic and go up to find it’s perfect dominant tone, so on and so on, you find 12 tones before you make it back around to an octave of the original tonic tone.
You don’t have to believe me, just listen to Leonard Bernstein:

 

[Papageno]

I’m going to disagree with this. The 12 tone system comes from the tonic/dominant relationship. Start with any tone(tonic), go up to the dominant that is “perfect” because it does not beat with the tonic, then use that tone as the tonic and go up to find it’s perfect dominant tone, so on and so on, you find 12 tones before you make it back around to an octave of the original tonic tone.
You don’t have to believe me, just listen to Leonard Bernstein:

Come on! On this video Bernstein explains the circle 5ths on the piano. So of course, he gets the tempered 12 tone chromatic scale.

If he would have explained the circle of 5ths using just intonation on a violin he would not have obtained the same note (7 octaves higher) after playing 12 just 5ths!

This is because (3/2)^12 = 129.7463...
whereas 2^7 = 128

No genius of music can change facts.

 

[iiipopes]

I’m going to disagree with this. The 12 tone system comes from the tonic/dominant relationship. Start with any tone(tonic), go up to the dominant that is “perfect” because it does not beat with the tonic, then use that tone as the tonic and go up to find it’s perfect dominant tone, so on and so on, you find 12 tones before you make it back around to an octave of the original tonic tone.
You don’t have to believe me, just listen to Leonard Bernstein:

No, it doesn't. By the time you get back around to the original tone, you are wayyyyyyyy sharp. EVERYTHING is tempered when you go that far around the cycle of fifths. There are twelve tones in the Western chromatic scale. Tuned "pure," each, in Pythagorean math, is 3/2 in frequency of the note before it, to avoid superhetrodyning, or commonly called, "beat" tones. 3/2^12, going up around the cycle of fifths of every semitone, back to the starting note, is @ 129.75, several octaves up from the starting note. The true octaves, with no superhetrodyning or beat tones to get to the same ascending note are the pure Pythagorean ratios of 2/1, which is the only constant in Western music, whatever the tempering or system of tuning. So to go up the same number of octaves to get to the same note going up by the cycle of fifths is 2^7, which is 128. So if you go up and completely around the cycle of fifths, by the time you get back to the octave of the note you started on, with no tempering, it is 129.75/128 sharp. This is noticable by even the least sensitive ear as grossly out of tune. No, EVERYTHING is tempered.

For more information, read the difinitive text on the subject, "On the Sensation of Tone" by Hemholz.

 

[MVE]

No, it doesn't. By the time you get back around to the original tone, you are wayyyyyyyy sharp. EVERYTHING is tempered when you go that far around the cycle of fifths. There are twelve tones in the Western chromatic scale. Tuned "pure," each, in Pythagorean math, is 3/2 in frequency of the note before it, to avoid superhetrodyning, or commonly called, "beat" tones. 3/2^12, going up around the cycle of fifths of every semitone, back to the starting note, is @ 129.75, several octaves up from the starting note. The true octaves, with no superhetrodyning or beat tones to get to the same ascending note are the pure Pythagorean ratios of 2/1, which is the only constant in Western music, whatever the tempering or system of tuning. So to go up the same number of octaves to get to the same note going up by the cycle of fifths is 2^7, which is 128. So if you go up and completely around the cycle of fifths, by the time you get back to the octave of the note you started on, with no tempering, it is 129.75/128 sharp. This is noticable by even the least sensitive ear as grossly out of tune. No, EVERYTHING is tempered.

For more information, read the difinitive text on the subject, "On the Sensation of Tone" by Hemholz.

Yes, I am well aware of that.
I was responding to the post stating there should really be 43 subdivisions between octaves.
I was only explaining why there are 12.
If you stack 5ths all the way around you would be sharp but it would still be recognizable as the original tone.
I think of tones more like colors. Pink and crimson are clearly different but they are both in the family of red. Does that make sense?

 

[La Faro]

No, it doesn't. By the time you get back around to the original tone, you are wayyyyyyyy sharp. EVERYTHING is tempered when you go that far around the cycle of fifths. There are twelve tones in the Western chromatic scale. Tuned "pure," each, in Pythagorean math, is 3/2 in frequency of the note before it, to avoid superhetrodyning, or commonly called, "beat" tones. 3/2^12, going up around the cycle of fifths of every semitone, back to the starting note, is @ 129.75, several octaves up from the starting note. The true octaves, with no superhetrodyning or beat tones to get to the same ascending note are the pure Pythagorean ratios of 2/1, which is the only constant in Western music, whatever the tempering or system of tuning. So to go up the same number of octaves to get to the same note going up by the cycle of fifths is 2^7, which is 128. So if you go up and completely around the cycle of fifths, by the time you get back to the octave of the note you started on, with no tempering, it is 129.75/128 sharp. This is noticable by even the least sensitive ear as grossly out of tune. No, EVERYTHING is tempered.

For more information, read the difinitive text on the subject, "On the Sensation of Tone" by Hemholz.

Any knowledge on stretch tuning?

 

[iiipopes]

If you stack 5ths all the way around you would be sharp but it would still be recognizable as the original tone.

And that is where we differ. I've done that, and it is not recognizable as the original tone. It sounds like a weird sharp note between notes.

 

[iiipopes]

Any knowledge on stretch tuning?

Stretch tuning is more applicable to pianos, since they essentially run the range of human hearing, and have to take into account psychoacoustic aspects as well as actual mathematical aspects beyond the equally tempered 2^(1/12) math of semitones. Moreover, because of the phenomenon of inharmonicity, as described by Dr. Kemp at St. Andrew's University, Scotland, the overtones of the strings are not perfect, either. Links:

Living Pianos
How to Tune a Piano, the Piano Tuning Tutorial
What is happening when we use stretch tuning?
https://link.springer.com/epdf/10.1...Pk-hurhBoR_MGlhA77XV8ub1EUrJoR6421SpYRJcjIw==

 

[La Faro]

Cool, so do you know how other instruments deal with being played with a stretched tune piano. Does a bass tune to it and not a pedal tuner, Do higher instruments do the same, flutes, saxes for example?

What happens when you put a synth on top of the piano. does it they just ignore each others tuning?

 

[MVE]

Any knowledge on stretch tuning?

Yes, stretch tuning is done to balance the overtones that are heard behind the fundamental tone.
When a piano string is hit, it is hit on a harmonic node. It rings out the fundamental tone plus many other tones at lower volumes but higher pitches.
Those harmonics are not in tune because the thickness and length of the string has to be compromised from its theoretical ideal. (A grand piano would need to be like 45’ long)
The more compromised the more out of tune the overtones become. That is why a small spinet piano needs to be stretched more than a grand. The overtones are sharp on the low notes and flat on the high notes. So for the higher notes a tuner might push the tuning of the fundamental well sharp to get the overtones closer to tune. If you think of every piano note actually being a chord made up of the fundamental and all overtones, stretching gets the whole chord closer to being in tune, even thought the fundamental tone is not.

 

[MVE]

Cool, so do you know how other instruments deal with being played with a stretched tune piano. Does a bass tune to it and not a pedal tuner, Do higher instruments do the same, flutes, saxes for example?

What happens when you put a synth on top of the piano. does it they just ignore each others tuning?

No, if the piano is stretched properly it will "sound" to the listener to be in tune with those other instruments much more than if the strings were tuned purely to the fundamental.

 

[La Faro]

But if it's bass notes are tunes flat and treble notes sharp, when it plays those notes, at the same time as bass a treble instruments, they are out of tune.

 

[MVE]

But if it's bass notes are tunes flat and treble notes sharp, when it plays those notes, at the same time as bass a treble instruments, they are out of tune.

Again, you need to think of each piano key as actually playing a chord made up of multiple tones. Their average, and the overall chord, is much closer to being in tune than they would be if the only the fundamental tone were in perfect tune.